```python
# Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline

# Custom CUDA kernel for matrix-scalar multiplication (C = A * s).
# This op is purely memory-bound, so the kernel uses float4 vectorized
# loads/stores to saturate memory bandwidth, with a small tail kernel
# to handle any remaining elements.
scalar_mul_cuda_source = """
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <cuda_runtime.h>

__global__ void scalar_mul_vec4_kernel(const float4* __restrict__ A,
                                       float4* __restrict__ C,
                                       const float s,
                                       const long n4) {
    long idx = blockIdx.x * (long)blockDim.x + threadIdx.x;
    if (idx < n4) {
        float4 v = A[idx];
        v.x *= s;
        v.y *= s;
        v.z *= s;
        v.w *= s;
        C[idx] = v;
    }
}

__global__ void scalar_mul_tail_kernel(const float* __restrict__ A,
                                       float* __restrict__ C,
                                       const float s,
                                       const long n) {
    long idx = blockIdx.x * (long)blockDim.x + threadIdx.x;
    if (idx < n) {
        C[idx] = A[idx] * s;
    }
}

torch::Tensor scalar_mul_cuda(torch::Tensor A, double s) {
    TORCH_CHECK(A.is_cuda(), "A must be a CUDA tensor");
    TORCH_CHECK(A.scalar_type() == torch::kFloat32, "A must be float32");

    auto A_c = A.contiguous();
    auto C = torch::empty_like(A_c);

    const long n = A_c.numel();
    if (n == 0) {
        return C;
    }

    const float sf = static_cast<float>(s);
    cudaStream_t stream = at::cuda::getCurrentCUDAStream();

    const long n4 = n / 4;
    const long rem = n - n4 * 4;

    if (n4 > 0) {
        const int block_size = 256;
        const long num_blocks = (n4 + block_size - 1) / block_size;
        scalar_mul_vec4_kernel<<<num_blocks, block_size, 0, stream>>>(
            reinterpret_cast<const float4*>(A_c.data_ptr<float>()),
            reinterpret_cast<float4*>(C.data_ptr<float>()),
            sf, n4);
    }

    if (rem > 0) {
        scalar_mul_tail_kernel<<<1, (int)rem, 0, stream>>>(
            A_c.data_ptr<float>() + n4 * 4,
            C.data_ptr<float>() + n4 * 4,
            sf, rem);
    }

    return C;
}
"""

scalar_mul_cpp_source = "torch::Tensor scalar_mul_cuda(torch::Tensor A, double s);"

# Compile the inline CUDA extension
scalar_mul = load_inline(
    name="scalar_mul_ext",
    cpp_sources=scalar_mul_cpp_source,
    cuda_sources=scalar_mul_cuda_source,
    functions=["scalar_mul_cuda"],
    verbose=False,
)


class ModelNew(nn.Module):
    """
    Optimized model that performs matrix-scalar multiplication (C = A * s)
    using a custom vectorized CUDA kernel.
    """
    def __init__(self):
        super(ModelNew, self).__init__()

    def forward(self, A: torch.Tensor, s: float) -> torch.Tensor:
        return scalar_mul.scalar_mul_cuda(A, s)
```